"mid"shipman in"cest"; a slang term for the act of a mishipman getting "together", personally or sexually, with a fellow midshipman from the same unit/school; usually used by any military unit that is training midshipmen such as the Naval Academy or Navy Reserve Officer Training Corps (NROTC).

Gunnery Sergeant: There will be no midcest whatsover going on in during this training, do you understand!?